By Professor Igor Shparlinski

Journal articles

Ostafe A; Shparlinski IE; Voloch JF, 2023, 'Equations and Character Sums with Matrix Powers, Kloosterman Sums over Small Subgroups, and Quantum Ergodicity', International Mathematics Research Notices, 2023, pp. 14196 - 14238, http://dx.doi.org/10.1093/imrn/rnac226

Shparlinski IE, 2023, 'Fixed points of the subset sum pseudorandom number generators', Designs Codes and Cryptography, 91, pp. 2473 - 2479, http://dx.doi.org/10.1007/s10623-023-01209-5

Dąbrowski A; Pomykała J; Shparlinski IE, 2023, 'On oracle factoring of integers', Journal of Complexity, 76, http://dx.doi.org/10.1016/j.jco.2023.101741

Kaminski M; Shparlinski IE; Waldschmidt M, 2023, 'On sets of linear forms of maximal complexity', Computational Complexity, 32, http://dx.doi.org/10.1007/s00037-022-00234-5

Chen C; Kerr B; Maynard J; Shparlinski IE, 2023, 'Metric theory of Weyl sums', Mathematische Annalen, 385, pp. 309 - 355, http://dx.doi.org/10.1007/s00208-021-02352-x

Bag N; Shparlinski IE, 2023, 'Bounds on bilinear sums of Kloosterman sums', Journal of Number Theory, 242, pp. 102 - 111, http://dx.doi.org/10.1016/j.jnt.2022.07.006

Chen C; Shparlinski IE, 2023, 'Hybrid Bounds on Two-Parametric Families of Weyl Sums Along Smooth Curves', Michigan Mathematical Journal, 73, pp. 123 - 139, http://dx.doi.org/10.1307/MMJ/20205904

Konyagin SV; Sha M; Shparlinski IE; Stewart CL, 2023, 'On the distribution of multiplicatively dependent vectors', Mathematical Research Letters, 30, pp. 509 - 540, http://dx.doi.org/10.4310/MRL.2023.v30.n2.a7

Shparlinski IE, 2023, 'On the Glasner property for matrices with polynomial entries', Journal of Number Theory, 242, pp. 522 - 531, http://dx.doi.org/10.1016/j.jnt.2022.04.015

Brandes J; Shparlinski IE, 2023, 'Two-dimensional Weyl sums failing square-root cancellation along lines', Arkiv for Matematik, 61, pp. 267 - 276, http://dx.doi.org/10.4310/ARKIV.2023.v61.n2.a1

Shkredov ID; Shparlinski IE; Zaharescu A, 2022, 'Bilinear Forms with Modular Square Roots and Twisted Second Moments of Half Integral Weight Dirichlet Series', International Mathematics Research Notices, 2022, pp. 17431 - 17474, http://dx.doi.org/10.1093/imrn/rnab220

Bagshaw C; Shparlinski IE, 2022, 'Energy bounds, bilinear forms and their applications in function fields', Finite Fields and their Applications, 82, http://dx.doi.org/10.1016/j.ffa.2022.102048

Ostafe A; Shparlinski IE; Pottmeyer L, 2022, 'Perfect powers in value sets and orbits of polynomials', The New York Journal of Mathematics, 27, pp. 903 - 917

Ostafe A; Shparlinski IE, 2022, 'On the Skolem problem and some related questions for parametric families of linear recurrence sequences', Canadian Journal of Mathematics, 74, pp. 773 - 792, http://dx.doi.org/10.4153/S0008414X21000080

Baker RC; Munsch M; Shparlinski IE, 2022, 'Additive energy and a large sieve inequality for sparse sequences', Mathematika, 68, pp. 362 - 399, http://dx.doi.org/10.1112/mtk.12140

Ghioca D; Shparlinski IE, 2022, 'Order of torsion for reduction of linearly independent points for a family of Drinfeld modules', Journal of Number Theory, 233, pp. 112 - 125, http://dx.doi.org/10.1016/j.jnt.2021.06.006

Baker RC; Chen C; Shparlinski IE, 2022, 'Large Weyl sums and Hausdorff dimension', Journal of Mathematical Analysis and Applications, 510, pp. 1 - 46, http://dx.doi.org/10.1016/j.jmaa.2022.126030

Ghioca D; Ostafe A; Saleh S; Shparlinski IE, 2022, 'On sparsity of representations of polynomials as linear combinations of exponential functions', Journal of the London Mathematical Society, 105, pp. 2076 - 2103, http://dx.doi.org/10.1112/jlms.12554

Banks W; Shparlinski I, 2022, 'On a conjecture of Soundararajan', Bulletin of the London Mathematical Society, 54, pp. 301 - 317, http://dx.doi.org/10.1112/blms.12524

Shparlinski IE, 2022, 'Bilinear sums of Gauss sums', Acta Arithmetica, 202, pp. 379 - 388, http://dx.doi.org/10.4064/aa210523-3-2

Shparlinski IE, 2022, 'MULTIPLICATIVE PROPERTIES of HILBERT CUBES', SIAM Journal on Discrete Mathematics, 36, pp. 1064 - 1070, http://dx.doi.org/10.1137/22M1470396

Kerr B; Mérai L; Shparlinski IE, 2022, 'On digits of Mersenne numbers', Revista Matematica Iberoamericana, 38, pp. 1901 - 1925, http://dx.doi.org/10.4171/RMI/1316

Ghioca D; Ostafe A; Saleh S; Shparlinski IE, 2021, 'A SPARSITY RESULT for the DYNAMICAL MORDELL-LANG CONJECTURE in POSITIVE CHARACTERISTIC', Bulletin of the Australian Mathematical Society, 104, pp. 381 - 390, http://dx.doi.org/10.1017/S0004972721000083

Shparlinski IE, 2021, 'Bounds of trilinear sums with Kloosterman fractions', Archiv Der Mathematik, 117, pp. 261 - 266, http://dx.doi.org/10.1007/s00013-021-01623-y

Mérai L; Ostafe A; Shparlinski IE, 2021, 'Dynamical irreducibility of polynomials modulo primes', Mathematische Zeitschrift, 298, pp. 1187 - 1199, http://dx.doi.org/10.1007/s00209-020-02630-5

Karpinski M; Shparlinski IE, 2021, 'Noisy polynomial interpolation modulo prime powers', Journal of Complexity, 64, http://dx.doi.org/10.1016/j.jco.2020.101542

Chen C; Shparlinski IE, 2021, 'Small values of Weyl sums', Journal of Mathematical Analysis and Applications, 495, http://dx.doi.org/10.1016/j.jmaa.2020.124743

Sha M; Shparlinski IE, 2021, 'Möbius Randomness Law for Frobenius Traces of Ordinary Curves', Canadian Mathematical Bulletin, 64, pp. 192 - 203, http://dx.doi.org/10.4153/S0008439520000363

Mérai L; Shparlinski IE, 2021, 'On the dynamical system generated by the Möbius transformation at prime times', Research in Mathematical Sciences, 8, pp. 10, http://dx.doi.org/10.1007/s40687-021-00249-4

Bag N; Shparlinski IE, 2021, 'Bounds of some double exponential sums', Journal of Number Theory, 219, pp. 228 - 236, http://dx.doi.org/10.1016/j.jnt.2020.09.020

Shparlinski IE, 2021, 'On the arithmetic structure of rational numbers in the cantor set', Bulletin of the Australian Mathematical Society, 103, pp. 22 - 27, http://dx.doi.org/10.1017/S0004972720000386

Shparlinski IE; Stewart CL, 2021, 'Counting solvable s-unit equations', Proceedings of the American Mathematical Society, 149, pp. 5119 - 5129, http://dx.doi.org/10.1090/proc/15674

Shparlinski IE; Wang Q, 2021, 'Exponential sums with sparse polynomials over finite fields', SIAM Journal on Discrete Mathematics, 35, pp. 976 - 987, http://dx.doi.org/10.1137/20M1357731

Kerr B; Mello J; Shparlinski IE, 2021, 'On elements of large order on elliptic curves and multiplicative dependent images of rational functions over finite fields', Illinois Journal of Mathematics, 65, pp. 499 - 514, http://dx.doi.org/10.1215/00192082-9043478

Shparlinski IE, 2020, 'Geometric progressions in vector sumsets over finite fields', Finite Fields and their Applications, 68, http://dx.doi.org/10.1016/j.ffa.2020.101747

Macourt S; Petridis G; Shkredov ID; Shparlinski IE, 2020, 'BOUNDS of TRILINEAR and TRINOMIAL EXPONENTIAL SUMS', SIAM Journal on Discrete Mathematics, 34, pp. 2124 - 2136, http://dx.doi.org/10.1137/20M1325502

Di Benedetto D; Garaev MZ; Garcia VC; Gonzalez-Sanchez D; Shparlinski IE; Trujillo CA, 2020, 'New estimates for exponential sums over multiplicative subgroups and intervals in prime fields', Journal of Number Theory, 215, pp. 261 - 274, http://dx.doi.org/10.1016/j.jnt.2020.02.004

Chen C; Shparlinski IE, 2020, 'Hausdorff dimension of the large values of Weyl sums', Journal of Number Theory, 214, pp. 27 - 37, http://dx.doi.org/10.1016/j.jnt.2020.04.023

Chen C; Shparlinski IE, 2020, 'On large values of Weyl sums', Advances in Mathematics, 370, http://dx.doi.org/10.1016/j.aim.2020.107216

Liu K; Shparlinski IE; Zhang T, 2020, 'Average distribution of k-free numbers in arithmetic progressions', Mathematische Nachrichten, 293, pp. 1505 - 1514, http://dx.doi.org/10.1002/mana.201900006

Gómez-Pérez D; Mérai L; Shparlinski IE, 2020, 'On the complexity of exact counting of dynamically irreducible polynomials', Journal of Symbolic Computation, 99, pp. 231 - 241, http://dx.doi.org/10.1016/j.jsc.2019.06.001

Konyagin SV; Makarychev SV; Shparlinski IE; Vyugin IV, 2020, 'On the Structure of Graphs of Markoff Triples', Quarterly Journal of Mathematics, 71, pp. 637 - 648, http://dx.doi.org/10.1093/qmathj/haz055

, 2020, 'Corrections to: Value sets of sparse polynomials (Canad. Math. Bull. (2020) 63 (187–196) DOI: 10.4153/S0008439519000316)', Canadian Mathematical Bulletin, 65, pp. 1071 - 1073, http://dx.doi.org/10.4153/S0008439521000928

Shparlinski IE; Voloch JF, 2020, 'Value Sets of Sparse Polynomials', Canadian Mathematical Bulletin, 63, pp. 187 - 196, http://dx.doi.org/10.4153/S0008439519000316

Kerr B; Shparlinski IE, 2020, 'Bilinear sums of Kloosterman sums, multiplicative congruences and average values of the divisor function over families of arithmetic progressions', Research in Number Theory, 6, http://dx.doi.org/10.1007/s40993-020-0191-9

Shparlinski I; Pakovich F, 2020, 'Level curves of rational functions and unimodular points on rational curves.', Proceedings of the American Mathematical Society, 148, pp. 1829 - 1833, http://dx.doi.org/10.1090/proc/14928

Pakovich F; Shparlinski IE, 2020, 'Level curves of rational functions nd unimodular points on rational curves', Proceedings of the American Mathematical Society, 148, pp. 1829 - 1833, http://dx.doi.org/10.1090/proc/14928

Shparlinski IE, 2020, 'Orders of points in families of elliptic curves', Proceedings of the American Mathematical Society, 148, pp. 2371 - 2377, http://dx.doi.org/10.1090/proc/14901

Shparlinski I; Korolev M, 2020, 'Sums of algebraic trace functions twisted by arithmetic functions.', Pacific J. Math., 304, pp. 505 - 18, http://dx.doi.org/10.2140/pjm.2020.304.505

Korolev M; Shparlinski I, 2020, 'Sums of algebraic trace functions twisted by arithmetic functions', Pacific Journal of Mathematics, 304, pp. 505 - 522, http://dx.doi.org/10.2140/pjm.2020.304.505

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